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5 moles of oxygen are heated at constant volume from \( 10^{0} C \) to \( 20^{0} C . \) The change in internal energy of the gas is: \( C_{p}=7.03 \mathrm{cal} \mathrm{mol}^{-1} \mathrm{K}^{-1} \) and \( R= \) \( 8.31 J \mathrm{mol}^{-1} \mathrm{K}^{-1} \)

1. 125 call \( l \)
2. 252 call
3. 50 call
4. 500 call

Correct answer: 50 call

Solution

For an ideal gas, the internal energy change depends only on temperature: \(\Delta U=nC_v\Delta T\). Since \(C_v=C_p-R\), converting \(R\) to cal mol\(^{-1}\)K\(^{-1}\) gives a value that leads to about 50 cal for 5 moles over a 10 K rise.

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